How to Handle Maths Anxiety: Discover the Joy of Mathematics
LikeHave you ever suffered anxiety because of your maths classes? Maths anxiety is the result of a very common misconception. We all grow up with stories of great scientists and mathematicians who appear to be superheroes. For example, we learn how Isaac Newton, while relaxing under an apple tree, invented physics and even came up with calculus. Or we learn about the great German mathematician Carl Friedrich Gauss who, while other children played football, did long sums in his head. We even remember watching the popular film about Alan Turing, who builds a supercomputer that helps end World War II while solving crossword puzzles!
So the message to the rest of us is that there are two categories of people: the lucky few who look at a differential equation and, after a few seconds, announce its solution; and the rest of us who look at a problem in elementary geometry as if it came from an alien civilization. And so we convince ourselves that since no answer came to our heads after reading the problem, we are not suited to do mathematics and should instead find an easier subject (e.g., reading telephone numbers or tying shoelaces).
This prejudice, like all prejudices, is the result of the belief in fairy tales that have nothing to do with the real world. And it is not just prevalent in mathematics or the sciences; great fiction writers like Stephen King or great tennis players like Roger Federer are viewed as superheroes. Like Superman, they were born with unique talents and once in front of a typewriter or on a tennis court (hopefully with a good racket), they were excellent. The rest of us are only like that when given unlimited refills in a fast-food restaurant.
This prejudice is not just insulting to you and me; it is also insulting to the great mathematicians, tennis players, etc. If someone is born with such amazing abilities, then what's so special about them? I have brown hair; my mother and father gave me the genes responsible for brown hair. If I bragged to you, "Look at me, I have brown hair, I made it myself," you would think I was mad. So if Albert Einstein got the clever genes from his mum and dad and then came up with the Theory of Relativity, is it really any achievement? And, let’s face it, he got a lucky break while working for the Swiss Patent Office, which at the time was dealing with the problem of synchronizing clocks.
The truth is very different. Yes, we all need a lucky break and perhaps some of us are a bit more clever than the rest. But the only thing that makes one of us a “genius” is what the ancient Greeks called “entelechy”. We would call this “the thing we love to do”; think of a child who gets a cheap guitar as a present (one string is missing) and then spends hours and hours trying to learn it. Perhaps when she grows up, she will not become famous like Eric Clapton; but she is already a guitar genius. By the time she is twenty, she will have mastered the instrument, and yet she will still enjoy playing the guitar for hours. Her dad is begging her to get a “proper job,” but she knows she has the best job in the world.
The same is true about mathematics: if you love the subject, you will not mind spending long hours studying esoteric theorems and going through derivations that seem to always hit a brick wall. This is not because you believe you are some sort of genius about to square the circle. It is simply because you love those squiggly symbols on your notebook, because concepts like vectors or complex numbers take you on amazing journeys. Yes, there is Netflix, but one can have a lot more fun trying to understand the limit of a function.
There is another important truth about mathematics. Daniel Kahneman, the distinguished psychologist, talks about two types of thinking: fast and slow. An example of fast thinking is when we are asked to choose a restaurant; in my case, the local burger joint comes to my mind as fast as lightning. An example of slow thinking (in my case, quasistatic thinking) is when we are asked to calculate “643 times 192”; we need to sit down, try to break the problem into many simple steps, and eventually come up with the answer (123456).
Mathematics is all about slow thinking! By slow thinking, I do not mean just in terms of time. I am mainly thinking about asking all sorts of questions that most people would never ask, and some would think they are a bit silly. For example, we all know that 2 times 3 is the same number as 3 times 2. None of us would spend any time thinking, “That's really amazing, who would have thought of that?”. But if you love mathematics, you will wonder why this is the case; for example, 2 minus 3 is not the same as 3 minus 2. But replace the minus sign with a multiplication sign and the rules change! As we begin to ask questions about things we take for granted, we pick up the habits that distinguish people who love maths. Perhaps we might discover that the first people who found out that 23=32 were Egyptian farmers who did not lose any money!
The author of any good textbook on mathematics will tell you that you do not learn mathematics by reading. Mathematics is all about doing. The first time you start to work on a problem, you discover you know very little (even though you went through fifty pages of material). You go back and forth, wonder if there is an error in the question, and eventually want to call a friend. That is how we learn (and please don't call a friend too soon)! We don't learn from our success; it is fleeting. We learn by stumbling on a difficult problem and persevering through it. We don't see the difficulty of the problem as an enemy; it is our friend, and we keep asking questions, poking at it from different angles. We go for a walk (or play backgammon), and then suddenly we have an idea. No, we are not developing supernatural abilities. We are just increasing our appreciation of the subject, and when we ask questions, we eventually get an answer.
After we master a problem, it seems to become too easy, and when we encounter a different version, we seem to produce a solution almost instinctively. But this is the result of practice, practice, practice, in the same way that a football player makes a long pass seem effortless. There is no natural gift that makes this happen; only our love for mathematics can ensure that we keep on practising.
On this note, beware of people who tell you that you can only improve in maths if you “work hard”. Bodybuilders talk about "no pain, no gain." And it is true that if you wanted to become Mr. Olympia, you have to go through some physical pain. But that is the whole point: it’s just physical pain! A bodybuilder loves what he does; he cannot wait to go back to the gym and spend five hours opposing gravity. Imagine if someone was forced to go through endless hours of lifting barbells. Yes, perhaps they would develop a good physique. But they would feel that they have no control over their life, that they are living someone else’s dream.
Mathematics is great fun! We live in an age where we are encouraged to think fast. Our smartphones produce endless gossip disguised as opinions. We have vast volumes of entertainment on our computer screens that allow us to switch our minds off. "Don't bother to think, to question," they tell us, "just go with the flow and have fun." But the greatest enjoyment does not come from ready-made recipes and pretentious slogans. It comes from engaging one of our greatest gifts, rational thinking. We humans do not have the impressive instincts of a lion who is at a superb balance with its environment. Instead, we have this trembling light, our mind. It tries to comprehend the world; like all of us, our ancestors most of the time encountered dead ends where the rational mind crashed against steel-reinforced walls. But eventually, someone standing on the shoulders of giants managed to go over that wall (only attempt to go through a wall if you are a quantum system). Our ancestors discovered fire not through some genius leap of transcendental thinking, but by asking the simple, almost silly questions that children ask. In our early years, we all are born with this ability, but unfortunately, a lot of us seem to lose it at some point. Keep asking those silly questions! Don't be satisfied with the easy answers. Remember what Richard Feynman said: “Science is the belief in the ignorance of experts.”
To conclude: take a break from school lessons and online tutorials. Take some time off from watching TV or scrolling through your smartphone and find a maths problem you like. These days, you don't need to buy a book; the internet is full of resources. Spend time thinking about it and never feel that your lack of understanding is a problem. You are actually doing great; you are thinking! Your greatest gift, what distinguishes us humans, is now engaged with the world. Okay, you might hear that your friend John (he is a scholar and a chorister) solved it while building a treehouse. But you should not care about that as long as you are learning. Running around the park is not about becoming Mo Farah; it’s about getting fitter.
Follow this recipe even when dealing with exams. Yes, it is possible that the upcoming maths paper was written by someone who thinks group theory should be taught at reception. At the end of the exam, you are unsure if you got more than fifty percent. You feel like you have not done well. But you have! You prepared as much as you could; you enjoyed working on those problems and tried to learn some new areas of maths. Sure, you encountered some difficult questions, but this does not reflect badly on you. However good we are, there is always a challenge around the corner that will remind us we are still human beings.